Decide whether (x + 1) is a factor of the polynomial (x3 + x2-x-1) or not.

Answer:

Given (x + 1) and (x3 + x2 – x – 1)

Using factor theorem

x + 1 = 0

x = 0 – 1

x = -1

Let

p(x) = (x3 + x2 – x – 1)

p(-1) = [(-1)3 + (-1)2 – (-1) – 1]

p(-1) = -1 + 1 + 1 – 1

p(-1) = 0

∴ (x + 1) is a factor of (x3 + x2 – x – 1)

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